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									GEOMETRY                    PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                  2010 - 2011
Module 1       Start: 8/19/2010 Teaching Days: 27               Test: 9/27/2010        Remediation Days: 1 End: 9/24/2010
                  Student Learning Expectation                                                       Task Analysis                                                 Vocabulary
1. Enduring Understanding - Points, lines, and planes are the foundations of geometry.
1a. Essential Question - Why are the following considered to be undefined terms in geometry: point, line, and plane?
LG.1.G.2                  Represent points, lines, and planes pictorally *identify points, lines, segments, rays, angles, and planes using models         point
                          with proper identification, as well as basic   *draw, label, and use proper symbol notation to represent the undefined          line
                          concepts derived from these undefined terms, terms points, lines, and planes in addition to rays, segments, and angles          plane
                          such as segments, rays, and angles                                                                                              segment
                                                                                                                                                          ray
                                                                                                                                                          angle
                                                                                                                                                          conjecture
                                                                                                                                                          colinear points
                                                                                                                                                          coplanar points
National Core:            G.CO.1                                           Know precise definitions of angle, circle, perpendicular line, parallel
                                                                           line, and line segment, based on the undefined notions of point, line,
                                                                           distance along a line, and distance around a circular arc.

Resources:                G. 1-1 pg.6; 1-4 pg.29; supplemental-origami box; wkst Drawing Intersections;          MCO---Students will give examples of points, lines, and planes and
                          relationships ofgeometric figures (parallel, perpendicular, angle relationships, etc) from objects found in nature. Students will bring items to class and have
                          classmates identify the term being modeled.

Assessments:
                          click here
LG.1.G.4                  Apply, with and without appropriate              *define and identify complementary angles, supplementary angles,               theorem
                          technology, definitions, theorems, properties,   vertical angles, linear pair of angles, and right angles                       postulate
                          and postulates related to such topics as         *determine relationships between angles formed by intersecting lines           corollary
                          complementary, supplementary, vertical           *find measures of angles using relationships                                   complementary angles
                          angles, linear pairs, and angles formed by       *use technology (scientific calculator, graphing calculator, Geogebra, etc.)   supplementary angles
                          perpendicular lines                              to reinforce concepts                                                          vertical angles
                                                                                                                                                          adjacent angles
                                                                                                                                                          consecutive angles
                                                                                                                                                          linear pair of angles
                                                                                                                                                          perpendicular lines
                                                                                                                                                          right angles

Resources:                G. 1-5 pg.37; MCO---Use ceiling tiles numbered and lettered for each type angle, later to be used for transversals; wkst. Angles and the Hands of Time;
                          Finding Missing Angles; Measuring Angles with a Protractor; later with chapter 4


Assessments:
                          click here
           Page 1 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
2. Enduring Understanding - Geometric figures can be represented in the coordinate plane.
2a. Essential Question - How can the relationships of lines be verified using the coordinate plane?
CGT.5.G.1a             Use coordinate geometry to find the distance   *calculate the midpoint and distance on the number line and between two      coordinate geometry
                       between two points and the midpoint of a       points                                                                       coordinate plane
                       segment                                        *calculate the midpoint and distance between two points on the               midpoint of a segment
                                                                      coordinate plane                                                             distance formula
                                                                                                                                                   midpoint formula

National Core:         G.PE.4                                         Use coordinates to prove simple geometric theorems algebraically. For
                                                                      example, prove or disprove that a figure defined by four given points in
                                                                      the coordinate plane is a rectangle; prove or disprove that the point (1,
                                                                      √3) lies on the circle centered at the origin and containing the point (0,
                                                                      2).

                       G.PE.5                                         Prove the slope criteria for parallel and perpendicular lines and use
                                                                      them to solve geometric problems (e.g., find the equation of a line
                                                                      parallel or perpendicular to a given line that passes through a given
                                                                      point).

Resources:             G. 1-3 pg.21; wkst Positioning Streets on a Map

Assessments:
                       click here
3. Enduring Understanding - Valid inductive and deductive reasoning are used to develop and prove conjectures.

3a. Essential Question - How does the application of logical reasoning facilitate understanding real-world situations?
LG.1.G.1a              Define inductive and deductive reasoning       *define inductive and deductive reasoning                                    inductive reasoning
                                                                                                                                                   deductive reasoning

Resources:             G. 2-1 pg.62 2-4 pg.82 deductive reasoning (omit laws of detachment, syllogism, and truth tables); wkst. Calculator Digits-Perpendicular and Parallel
                       Segments; NUMBER PATTERNS;

Assessments:
                       click here




        Page 2 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
LG.1.G.1b                 Make predictions or conjectures based on real     *extend patterns by various strategies                                   inductive reasoning
                          world situations using inductive reasoning        *make conclusions based on real world situations                         pattern
                          such as but not limited to:                       *make conjetures by various strategies including figural and numerical
                          * Using figural and numerical patterns            patterns
                          * Using observations
                          * Identifying counterexamples

Resources:                G. 2-1 pg.63 problems pg.64 Ch.2 Resource Enrichment pg.62

Assessments:
                          click here
LG.1.G.1c                 Make predictions or conjectures based on real     *read Venn diagrams                                                      inductive reasoning
                          world situations using deductive reasoning        *read a logic matrix                                                     deductive reasoning
                          and appropriate strategies such as but not        *draw and interpret Venn diagrams                                        Venn diagram
                          limited to: • Venn diagrams • Matrix logic        *draw and use logic matrix to state conclusions                          matrix logic
                                                                            *make conclusions based on real world situations                         conjecture


Resources:                G. pg.88 pg.69-70 problem pg.73 #41-44,Manipulatlives pg.46 Ch.2 Resource Enrichment pg.80; wkst. supplements;VENN FAMILY;             MCO----Students will
                          work in pairs to solve matrix logic puzzles and draw Venn diagrams.


Assessments:
                          click here
LG.1.G.1d                 Make predictions or conjectures based on real     *identify examples of Laws of Syllogism and Laws of Detachment           inductive reasoning
                          world situations using inductive and/or           *extend patterns by various strategies                                   deductive reasoning
                          deductive reasoning strategies such as but not    *write inverse, converse, and contrapositive when given a statement      conditional statement
                          limited to:                                       *determine equivalence of statement & contrapositive and of converse &   inverse
                          * Conditional statements (statement,              inverse                                                                  converse
                          converse, inverse, contrapositive)                *make conclusions based on real world situations                         contrapositive
                          * Laws of Syllogism and Laws of Detachment                                                                                 counterexample
                          * Identifying valid and invalid conclusions and                                                                            biconditional statement
                          arguments                                                                                                                  negation


Resources:                G. 2-3 pg.75 Manipulatives pg.41 Ch.2 Resource Enrichment pg.74; MCO---Student will work in groups to practice conditional statements. Students will
                          take turns writing a statement and the other members of the group will write the converse, inverse, and contrapositive.


Assessments:
                          click here
LG.1.G.3                  Describe relationships derived from geometric *identify figural patterns                                                   figural pattern
                          figures or figural patterns                   *extend patterns using various strategies                                    sequences
                                                                        *describe pattern relationships with symbols, words, and pictures


           Page 3 of 40                                                                Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
Resources:                vocabulary review Ch.1 Resource pg.50; example problems Ch.1 Angle Relationships pg.26; wkst. Figurate Numbers; wkst. Pascal's Triangle

Assessments:
                          click here
LG.1.G.6                  Give justification for conclusions reached by   *state basic theorems                                                       two-column proof
                          deductive reasoning; State and prove key        *justify or construct a basic proof, whether two-column, paragraph, or      paragraph proof
                          basic theorems in geometry (i.e., the           flow                                                                        flow proof
                          Pythagorean Theorem, the sum of the                                                                                         justify
                          measures of the angles of a triangle is 180°,
                          and the line joining the midpoints of two sides
                          of a triangle is parallel to the third side and
                          half its length)

National Core:            G.CO.9                                         Prove theorems about lines and angles. Theorems include: vertical
                                                                         angles are congruent; when a transversal crosses parallel lines, alternate
                                                                         interior angles are congruent and corresponding angles are congruent;
                                                                         points on a perpendicular bisector of a line segment are exactly those
                                                                         equidistant from the segment’s endpoints.


                          G.CO.10                                        Prove theorems about triangles. Theorems include: measures of interior
                                                                         angles of a triangle sum to 180°; base angles of isosceles triangles are
                                                                         congruent; the segment joining midpoints of two sides of a triangle is
                                                                         parallel to the third side and half the length; the medians of a triangle
                                                                         meet at a point.



Resources:                G. 2-5 pg.89; 2-6 pg.94; 2-7 pg.101; 2-8 pg.107; SCHOOL MATH; LINEUP LOGIC; MYSTERIES;            MCO----Students will be given an algebraic proof with
                          the statements and reason cut apart. Students will then reconstruct the proof by matching the statement with the correct property of equality and put
                          them in order.

Assessments:
                          click here
9 SLEs                                                                                                                                                                   End of Module 1


ALIGNMENT NOTES
                                                                                       Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together




           Page 4 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
                                                               Project for Quarter 1


The Angle Book Project
1. Make a foldable book following directions given.
2. Use example book as guide for students.
3. Use two days of classtime, due at latter part of 1st qtr.




         Page 5 of 40                                              Glencoe Geometry: 2005   127rgeorge@pcssdmail.org
GEOMETRY                 PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                    2010 - 2011
Module 2     Start: 9/27/2010 Teaching Days: 22                Test: 11/1/2010          Remediation Days: 1 End: 10/20/2010
                Student Learning Expectation                                                          Task Analysis                                                 Vocabulary
1. Enduring Understanding - Points, lines, and planes are the foundations of geometry.
1b. Essential Question - How can angle relationships be used to prove that two lines cut by a transversal are parallel?
LG.1.G.5a              Solve problems involving the parallel                *identify angle pairs created by parallel lines cut by a transversal          parallel lines
                       relationship of two lines in a plane that are cut    *deduce that vertical angles, corresponding angles, alternate interior        transversal
                       by a transversal                                     angles, and alternate exterior angles are congruent, and that same side       corresponding angles
                       •a pair of alternate interior, alternate exterior,   interior/exterior angles are supplementary                                    alternate interior/exterior angles
                       or corresponding angles are congruent                *use angle relationships to find missing angle measures                       same-side interior (consecutive
                       •consecutive (same-side) interior angles are         *use angle relationships to prove two lines cut by a transversal are          interior)
                       supplementary                                        parallel                                                                      same-side exterior (consecutive
                       •consecutive (same-side) exterior angles are         *use technology (scientific/graphing calculator, geogebra, etc) to teach or   exterior)
                       supplementary                                        reinforce concepts                                                            supplementary angles
                                                                                                                                                          congruent
                                                                                                                                                          skew lines


Resources:             G. 3-1 pg.126; use ceiling tiles with colored painters tape

Assessments:
                       click here
LG.1.G.5b              Solve problems involving the parallel            *identify angle pairs created by parallel lines cut by a transversal              parallel lines
                       relationship of two lines that are perpendicular *determine that vertical angles, corresponding angles, alternate interior         perpendicular lines
                       to the same line                                 angles, and alternate exterior angles are congruent, and that same side           transversal
                                                                        interior/exterior angles are supplementary                                        corresponding angles
                                                                        *use angle relationships to find missing angle measures                           alternate interior/exterior angles
                                                                        *use angle relationships to prove two lines cut by a transversal are              same-side interior (consecutive
                                                                        parallel                                                                          interior)
                                                                        *determine that two lines perpendicular to the same line are parallel             same-side exterior
                                                                        *solve problems with two lines perpendicular to the same lines being              supplementary angles
                                                                        parallel                                                                          congruent
                                                                        *use technology to reinforce concepts                                             skew lines


Resources:             G. 3-4 pg.134; Monopoly and Perpendicular and Parallel Lines; BUILD IT


Assessments:
                       click here
2. Enduring Understanding - Geometric figures can be represented in the coordinate plane.
2b. Essential Question - How can the relationships of lines be verified using the coordinate plane?


        Page 6 of 40                                                                    Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
CGT.5.G.1b             Use coordinate geometry to find the slopes of *determine the slope of a line using two points                                    coordinate geometry
                       parallel, perpendicular, horizontal, and vertical *determine the relationships of slopes of parallel and perpendicular lines,    coordinate plane
                       lines                                             and determine if lines are parallel, perpendicular, or intersecting            slope
                                                                         *distinguish when the graph of a line is vertical or horizontal based on       slope of parallel lines
                                                                         slope                                                                          slope of perpendicular lines
                                                                                                                                                        slope of horizontal lines
                                                                                                                                                        slope of vertical lines
                                                                                                                                                        slope formula
                                                                                                                                                        negative reciprocal

National Core:         G.PE.4                                            Use coordinates to prove simple geometric theorems algebraically. For
                                                                         example, prove or disprove that a figure defined by four given points in
                                                                         the coordinate plane is a rectangle; prove or disprove that the point (1,
                                                                         √3) lies on the circle centered at the origin and containing the point (0,
                                                                         2).


                       G.PE.5                                            Prove the slope criteria for parallel and perpendicular lines and use
                                                                         them to solve geometric problems (e.g., find the equation of a line
                                                                         parallel or perpendicular to a given line that passes through a given
                                                                         point).

Resources:             G. 3-3 pg.139; 3-4 pg.145

Assessments:
                       click here
CGT.5.G.2              Write the equation of a line parallel to a line   *determine the slope of the line parallel to a given line                      slope of parallel lines
                       through a given point not on the line             *use slope-intercept form or point-slope form to determine the y-intercept     slope-intercept form of a linear
                                                                         (b)                                                                            equation
                                                                         *write the equation of the line parallel to the given line through the given   standard form of a linear
                                                                         point in all possible forms                                                    equation
                                                                                                                                                        point-slope form of a linear
                                                                                                                                                        equation
Resources:             G. 3-3 pg.139; 3-4 pg.145


Assessments:
                       click here
CGT.5.G.3              Write the equation of a line perpendicular to a *determine the slope of the line perpendicular to a given line                   slope of perpendicular lines
                       line through a given point                      *use slope-intercept form or point-slope form to determine the y-intercept       slope-intercept form of a linear
                                                                       (b)                                                                              equation.
                                                                       *write the equation of the line perpendicular to the given line through the      standard form of a linear
                                                                       given point in all possible forms                                                equation
                                                                                                                                                        point-slope form of a linear
                                                                                                                                                        equation


        Page 7 of 40                                                                 Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Resources:                G. 3-3 pg.139; 3-4 pg.145

Assessments:
                          click here
4. Enduring Understanding - Similar geometric figures have proportional attributes
4a. Essential Question - How are relationships between congruent figures used to solve problems?
T.2.G.1a                  Apply SSS, SAS, ASA, AAS congruence           *identify properties of congruent figures                                  congruent polygons
                          correspondence to find missing parts of       *identify corresponding parts of triangles                                 corresponding parts
                          geometric figures and provide logical         *use theorems to prove triangles congruent                                 side angle side congruence
                          justification                                 *use proportions to find missing sides of figures                          angle side angle congruence
                                                                        *use properties to find missing angles                                     side side side congruence
                                                                                                                                                   angle angle side congruence


National Core:            G.CO.7                                        Explain and use the relationship between the sine and cosine of
                                                                        complementary angles.

Resources:                G. 4-4 pg.200; 4-5 pg.207; wkst. The Big Triangle Problem; wkst Angles of Triangles; wkst. Identifying what is needed to prove triangles are congruent;
                          patty paper wkst 126-139, 168,199

Assessments:
                          click here
5 SLEs                                                                                                                                                                End of Module 1


ALIGNMENT NOTES
                                                                                      Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together

                                                                              Project for Module 2




           Page 8 of 40                                                             Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
GEOMETRY                    PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                 2010 - 2011
Module 3           Teaching Days: 25 Test: 12/16/2010                Remediation Days: 1       End: 12/10/2010
                    Student Learning Expectation                                                       Task Analysis                                                Vocabulary
5. Enduring Understanding - Relationships that exist between the angles and sides of geometric figures can be
proven.
5a. Essential Question - How are properties of geometric figures related to their measurable attributes?
T.2.G.3a                  Identify and use the altitudes of triangles to   *identify altitude                                                             altitude of a triangle
                          solve problems                                   *state conclusions about angle measures and segment lengths when               orthocenter
                                                                           drawing altitudes                                                              perpendicular
                                                                           *apply concepts to basic proofs                                                geometric mean
                                                                           *examine orthocenters of various types of triangles
                                                                           *solve problems using properties of altitudes

National Core:            G.CO.12                                          Make formal geometric constructions with a variety of tools and
                                                                           methods (compass and straightedge, string, reflective devices,
                                                                           paper folding, dynamic geometric software, etc.). Copying a segment;
                                                                           copying an angle; bisecting a segment; bisecting an angle; constructing
                                                                           perpendicular lines, including the perpendicular bisector of a line segment;
                                                                           and constructing a line parallel to a given line through a point not on the
                                                                           line.

Resources:                G. 5-1 pg.238; patty paper wkst 37and 47


Assessments:
                          click here
T.2.G.3b                  Identify and use the medians of triangles to     *identify median                                                               median of a triangle
                          solve problems                                   *state conclusions about angle measures and segment lengths when               centroid
                                                                           drawing medians
                                                                           *solve problems using properties of medians
                                                                           *examine centroids of various types of triangles
                                                                           *apply concepts to basic proofs

National Core:            G.CO.12                                          Make formal geometric constructions with a variety of tools and
                                                                           methods (compass and straightedge, string, reflective devices,
                                                                           paper folding, dynamic geometric software, etc.). Copying a segment;
                                                                           copying an angle; bisecting a segment; bisecting an angle; constructing
                                                                           perpendicular lines, including the perpendicular bisector of a line segment;
                                                                           and constructing a line parallel to a given line through a point not on the
                                                                           line.




           Page 9 of 40                                                                Glencoe Geometry: 2005                                                    127rgeorge@pcssdmail.org
Resources:                 G. 5-1 pg.238; wkst. Medians of Triangles; patty paper wkst 36

Assessments:
                           click here
T.2.G.3c                   Identify and use the angle bisectors of        *identify angle bisector                                                       angle bisector
                           triangles to solve problems                    *state conclusions about angle measures and segment lengths when               incenter
                                                                          drawing angle bisectors
                                                                          *solve problems using properties of angle bisectors
                                                                          *examine incenters of various types of triangles
                                                                          *apply concepts to basic proofs

National Core:             G.CO.12                                        Make formal geometric constructions with a variety of tools and
                                                                          methods (compass and straightedge, string, reflective devices,
                                                                          paper folding, dynamic geometric software, etc.). Copying a segment;
                                                                          copying an angle; bisecting a segment; bisecting an angle; constructing
                                                                          perpendicular lines, including the perpendicular bisector of a line segment;
                                                                          and constructing a line parallel to a given line through a point not on the
                                                                          line.


Resources:                 G. 5-1 pg.238; patty paper wkst 34 and 45; MCO----Students will use quilt patterns, mosaics, or other artwork from various cultures to identify triangles
                           and the special segments of the triangles. Students my choose to create their own artwork using triangles and their segments.


Assessments:
                           click here
T.2.G.3d                   Identify and use the perpendicular bisectors of *identify perpendicular bisector                                              perpendicular bisector
                           triangles to solve problems                     *state conclusions about angle measures and segment lengths when              circumcenter
                                                                           drawing perpendicular bisectors
                                                                           *solve problems using properties of perpendicular bisectors
                                                                           *examine circumcenters of various types of triangles
                                                                           *apply concepts to basic proofs

National Core:             G.CO.12                                        Make formal geometric constructions with a variety of tools and
                                                                          methods (compass and straightedge, string, reflective devices,
                                                                          paper folding, dynamic geometric software, etc.). Copying a segment;
                                                                          copying an angle; bisecting a segment; bisecting an angle; constructing
                                                                          perpendicular lines, including the perpendicular bisector of a line segment;
                                                                          and constructing a line parallel to a given line through a point not on the
                                                                          line.


Resources:                 G. 5-1 pg.238; wkst. Triangles: The Points, Segments, and Angles; patty paper wkst 32 and wkst 43;       MCO---- Students will work with a partner and use
                           straws to build trianagles with special segments.


           Page 10 of 40                                                              Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Assessments:
                           click here
T.2.G.3e                   Identify and use the midsegments of triangles *identify midsegment                                                              midsegment
                           to solve problems                             *state conclusions about angle measures and segment lengths when
                                                                         drawing midsegments
                                                                         *solve problems using properties of midsegments
                                                                         *apply concepts to basic proofs

National Core:             G.CO.12                                          Make formal geometric constructions with a variety of tools and
                                                                            methods (compass and straightedge, string, reflective devices,
                                                                            paper folding, dynamic geometric software, etc.). Copying a segment;
                                                                            copying an angle; bisecting a segment; bisecting an angle; constructing
                                                                            perpendicular lines, including the perpendicular bisector of a line segment;
                                                                            and constructing a line parallel to a given line through a point not on the
                                                                            line.


Resources:                 G. pg.308; wksht Triangles: the points, segments, and angles; patty paper wkst 74


Assessments:
                           click here
5b. Essential Question - How can it be determined if three given segment measures will form a triangle?
T.2.G.2                    Investigate the measures of segments to          *create triangles using lengths of line segments                               Triangle Inequality Theorem
                           determine the existence of triangles (triangle   *investigate the measures of segments to determine the existence of
                           inequality theorem)                              triangles
                                                                            *state conclusions when applying the Triangle Inequality Theorem

Resources:                 G. 5-2 pg.247; 5-4 pg.261; spaghetti and paper

Assessments:
                           click here
4. Enduring Understanding - Indirect measurement is based on the properties of geometric figures.
4b. Essential Question - How are the relationships between similar figures used to solve problems?
M.3.G.4                    Given similar geometric objects, use             *identify properties of similar figures                                        similar figures/polygons
                           proportional reasoning to solve practical        *determine if figures are similar by setting up and solving proportions        scale drawing
                           problems (including scale drawings)              *use scale drawings and other information to solve real-world problems         geometric mean
                                                                            through proportional reasoning




           Page 11 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
National Core:           G.SRT.4                                         Prove theorems about triangles. Theorems include: a line parallel to one
                                                                         side of a triangle divides the other two proportionally, and conversely; the
                                                                         Pythagorean Theorem proved using triangle similarity.


                         G.SRT.5                                         Use congruence and similarity criteria for triangles to solve problems
                                                                         and to prove relationships in geometric figures.
                         G.GPE.6                                         Find the point on a directed line segment between two given points
                                                                         that partitions the segment in a given ratio.

                         G.MG.3                                          Apply geometric methods to solve design problems (e.g., designing
                                                                         an object or structure to satisfy physical constraints or minimize cost;
                                                                         working with typographic grid systems based on ratios).

Resources:               G. 6-2 pg.289; 6-3 pg.298; teacher to teacher pg.291; STICK FIGURES

Assessments:
                         click here
M.3.G.5a                 Identify and apply properties of and theorems *apply angle relationships of parallel lines cut by a transversal                parallel lines
                         about parallel and perpendicular lines to prove *apply angle relationships of perpendicular lines                              perpendicular lines
                         other theorems                                  *identify properties and theorems of parallel and perpendicular lines          theorems
                                                                         *prove theorems related to parallel and perpendicular lines

National Core:           G.SRT.4                                         Prove theorems about triangles. Theorems include: a line parallel to one
                                                                         side of a triangle divides the other two proportionally, and conversely; the
                                                                         Pythagorean Theorem proved using triangle similarity.


Resources:               G. 6-4 pg. 307: PATTERN BLOCKS

Assessments:
                         click here
8 SLEs                                                                                                                                                                    End of Module 1


ALIGNMENT NOTES
                                                                                       Notation
G.- Glencoe Textbook;
                                                                              Project for Module 3




         Page 12 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
GEOMETRY                     PULASKI CO. SPEC. SCHOOL DIST.                                                                                                                2010 - 2011
Module 4       Start: 1/3/2011 Teaching Days: 25                Test: 2/10/2011       Remediation Days: 1 End: 2/4/2011
                  Student Learning Expectation                                                       Task Analysis                                                  Vocabulary
4. Enduring Understanding - Indirect measurement is based on the properties of geometric figures.
4c. Essential Question - How are properties of right triangles used to find angle and side measurements?
T.2.G.4                    Apply the Pythagorean Theorem and its           *identify legs and hypotenuse of a right triangle                             Pythagorean Theorem
                           converse in solving practical problems          *solve equations using Pythagorean Theorem                                    hypotenuse
                                                                           *use Pythagorean Theorem to solve practical problems and express in           leg
                                                                           decimal and/or simplest radical form
                                                                           *given a, b and c, determine if a triangle is a right triangle given the
                                                                           lengths of the sides

National Core:             G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
                                                                           triangles in applied problems.

Resources:                 G. 7-2 pg.350; geoboard; wkst. The Pythagorean Theorem; wkst. What Type of Triangle?; MCO----Students will work in groups to draw right triangles to
                           solve real world problems that they have created. After the students in the group agree on the way to set up the problem each student will then apply the
                           Pythagorean Theorem or trignometic ratio to solve.

Assessments:
                           click here
T.2.G.5a                   Use the special right triangle relationship 30°- *describe the relationships between the length of sides of 30°-60°-90°       special right triangle
                           60°-90° to solve problems                        triangles
                                                                            *find the length of two sides of a 30°-60°-90° triangle when one side is
                                                                            given
                                                                            *apply the relationships of a 30°-60°-90° triangle to find missing side(s)
                                                                            and angle(s) in diagrams and word problems

Resources:                 G. 7-3 pg.357

Assessments:
                           click here
T.2.G.5b                   Use the special right triangle relationship 45°- *describe the relationships between the length of sides of 45°-45°-90°       special right triangle
                           45°-90° to solve problems                        triangles
                                                                            *find the length of two sides of a 45°-45°-90° triangle when one side is
                                                                            given
                                                                            *apply the relationships of a 45°-45°-90° triangle to find missing side(s)
                                                                            and angle(s) in diagrams and word problems
                                                                            *use the Isosceles Triangle Theorem and the Pythagorean Theorem to
                                                                            determine the lengths of sides of special right triangles



           Page 13 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
Resources:                 G. 7-3 pg.357 daily intervention differentiated instruction pg.358; wkst Right Triangles and Special Right Triangles


Assessments:
                           click here
T.2.G.6a                   Use trigonometric ratios (sine, cosine,         *apply trigonometric ratios of a right triangle given the length of one side trigonometric ratios
                           tangent) to determine lengths of sides in right and the measures of one acute angle to find the lengths of sides in right sine
                           triangles                                       triangles in giagrams and real-world problems                                cosine
                                                                                                                                                        tangent
                                                                                                                                                        hypotenuse
                                                                                                                                                        leg of a right triangle
                                                                                                                                                        opposite side
                                                                                                                                                        adjacent side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
                                                                           complementary angles.

                           G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
                                                                           triangles in applied problems.

Resources:                 G. 7-4 pg.364 Manipulatives pg.117-120

Assessments:
                           click here
T.2.G.6b                   Use trigonometric ratios (sine, cosine,         *apply trigonometric ratios given two sides and an angle measure in           trigonometric ratios
                           tangent) to determine measures of angles in     diagrams and real-world problems                                              sine
                           right triangles                                                                                                               cosine
                                                                                                                                                         tangent
                                                                                                                                                         hypotenuse
                                                                                                                                                         leg of a right triangle
                                                                                                                                                         opposite side
                                                                                                                                                         adjacent side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
                                                                           complementary angles.

                           G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
                                                                           triangles in applied problems.
Resources:                 G. 7-4 pg.364 Manipulatives pg.117-120

Assessments:
                           click here


           Page 14 of 40                                                                Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
T.2.G.6c                   Use trigonometric ratios (sine, cosine,         *identify angles of elevation and angles of depression                     trigonometric ratios
                           tangent) in right triangle problems involving   *use trig ratios to find side lengths and or angles of elevation or        sine
                           angles of elevation and depression              depression in diagrams and real-world problems                             cosine
                                                                                                                                                      tangent
                                                                                                                                                      angle of elevation
                                                                                                                                                      angle of depression
                                                                                                                                                      hypotenuse
                                                                                                                                                      leg of a right triangle
                                                                                                                                                      opposite side
                                                                                                                                                      adjacent side

National Core:             G.SRT.7                                         Explain and use the relationship between the sine and cosine of
                                                                           complementary angles.

                           G.SRT.8                                         Use trigonometric ratios and the Pythagorean Theorem to solve right
                                                                           triangles in applied problems.

Assessments:
                           click here
T.2.G.7                    Use similarity of right triangles to express the *identify similar triangle characteristics                                similarity
                           sine, cosine, and tangent of an angle in a right *set up proportions from similar triangles to find missing side lengths   sine
                           triangle as a ratio of given side lengths        *write trig ratios of similar triangles                                   cosine
                                                                                                                                                      tangent
                                                                                                                                                      angle of elevation
                                                                                                                                                      angle of depression

National Core:             G.SRT.6                                         Understand that by similarity, side ratios in right triangles are
                                                                           properties of the angles in the triangle, leading to definitions of
                                                                           trigonometric ratios for acute angles.

Resources:                 G. pg. 214-215

Assessments:
                           click here
5. Enduring Understanding - Relationships exist between the angles and sides of geometric figures.
5a. Essential Question - How are angles, sides, and diagonals of quadrilaterals related and applied?




           Page 15 of 40                                                                Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
R.4.G.1a                   Explore, verify and solve problems involving     *identify properties of quadrilaterals                                      quadrilaterals
                           the properties of quadrilaterals                 *determine properties of quadrilaterals with respect to parallel sides,     parallelograms
                           • Four sided polygon                             lengths of sides, diagonal measurements, and measurement of angles          rectangle
                                                                            *explore quadrilaterals and their properties to verify the type of figure   rhombus
                                                                            formed                                                                      square
                                                                            *solve problems involving the properties of quadrilaterals                  trapezoid
                                                                                                                                                        kite
                                                                                                                                                        isosceles trapezoid
                                                                                                                                                        consecutive sides/angles
                                                                                                                                                        opposite sides/angles
                                                                                                                                                        midsegments

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.

Resources:                 wkst. Sorting Quadrilaterals; wkst. Charts and Quadrilaterals; POLYGONS

Assessments:
                           click here
R.4.G.1b                   Explore, verify and solve problems involving     *identify properties of parallelograms                                      quadrilaterals
                           the properties of parallelograms                 *determine properties of parallelograms with respect to parallel sides,     diagonals
                           • Quadrilateral                                  length of sides, diagonal measurements, and measurement of angles           parallelograms
                           • Congruent opposite sides and opposite          *explore parallelograms and their properties to verify the type of figure   consecutive sides/angles
                           angles                                           formed                                                                      opposite sides/angles
                           • Consecutive angles are supplementary                                                                                       supplementary
                           • Diagonals bisect                                                                                                           bisect
                           • Two congruent triangles are formed by the
                           diagonals
                           • If there is one right angle, then all angles
                           are right angles.

National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.

Resources:                 G. 8-2 pg.411; Manipulatives pg.129;     MCO--- Students will investigate the clothing of various cultures looking for geometric designs that form different
                           polygons.




           Page 16 of 40                                                                Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
Assessments:
                           click here
R.4.G.1c                   Explore, verify and solve problems involving     *identify properties of parallelograms                                         quadrilaterals
                           the proof that a quadrilateral is a              *determine properties of parallelograms with respect to parallel sides,        parallelograms
                           parallelogram                                    length of sides, diagonal measurements, and measurement of angles              consecutive sides/angles
                           • Diagonals bisect each other                    *explore parallelograms and their properties to verify the type of figure      opposite sides/angles
                           • One pair of opposite sides is both congruent   formed                                                                         diagonals
                           and parallel                                                                                                                    bisect
                           • Both pairs of opposite sides are congruent
                           • Both pairs of opposide sides are parallel
                           • Both pairs of opposite angles are congruent


National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.

Resources:                 G. 8-3 pg.417; Manipulatives pg.132; Ch.2 Enrichment pg.434

Assessments:
                           click here
R.4.G.1d                   Explore, verify and solve problems involving     *identify properties of rectangles                                             quadrilaterals
                           the properties of rectangles                     *determine properties of rectangles with respect to parallel sides, length     parallelograms
                           • Same properties as parallelograms              of sides, diagonal measurements, and measurement of angles                     rectangle
                           • Four right angles                              *explore rectangles and their properties to verify the type of figure formed   consecutive sides/angles
                           • Congruent diagonals                                                                                                           opposite sides/angles
                                                                                                                                                           diagonals


National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.
Assessments:
                           click here
R.4.G.1e                   Explore, verify and solve problems involving     *identify properties of rhombi                                                 quadrilaterals
                           the properties of rhombi                         *determine properties of rhombi with respect to parallel sides, length of      parallelograms
                           • Same properties as parallelograms              sides, diagonal measurements, and measurement of angles                        rectangle
                           • All sides are congruent                        *explore rhombi and their properties to verify the type of figure formed       rhombus
                           • Diagonals are perpendicular                                                                                                   consecutive sides/angles
                           • Diagonlas bisect a pair of opposite angles                                                                                    opposite sides/angles
                                                                                                                                                           diagonal
                                                                                                                                                           perpendicular
                                                                                                                                                           bisect
           Page 17 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.


Resources:                 G. 8-5 pg.431; Ch.8 Resources pg.445

Assessments:
                           click here
R.4.G.1f                   Explore, verify and solve problems involving     *identify properties of squares                                                quadrilaterals
                           the properties of squares                        *determine properties of squares with respect to parallel sides, length of     parallelograms
                           • Same properties as parallelograms              sides, diagonal measurements, and measurement of angles                        rectangle
                           • Same properties as rectangles                  *explore squares and their properties to verify the type of figure formed      rhombus
                           • Same properties as rhombi                                                                                                     square
                                                                                                                                                           consecutive sides/angles
                                                                                                                                                           opposite sides/angles
                                                                                                                                                           diagonals
                                                                                                                                                           bisect
                                                                                                                                                           perpendicular


National Core:             G.CO.11                                          Prove theorems about parallelograms. Theorems include: opposite
                                                                            sides are congruent, opposite angles are congruent, the diagonals
                                                                            of a parallelogram bisect each other, and conversely, rectangles are
                                                                            parallelograms with congruent diagonals.


Resources:                 G. 8-5 pg.431; Manipulatives pg.135

Assessments:
                           click here
R.4.G.1g                   Explore, verify and solve problems involving     *identify properties of trapezoids                                             quadrilaterals
                           the properties of trapezoids                     *determine properties of trapezoids with respect to parallel sides, length     trapezoid
                           • Quadrilateral                                  of sides, diagonal measurements, and measurement of angles                     consecutive sides/angles
                           • One pair of opposite sides are parallel        *explore trapezoids and their properties to verify the type of figure formed   opposite sides/angles
                           • Midsegment is half the sum of the lengths of                                                                                  midsegments
                           the bases

Resources:                 G. 8-6 pg.439; patty paper wkst 76 and 84

Assessments:
                           click here


           Page 18 of 40                                                                Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
R.4.G.1h                   Explore, verify and solve problems involving    *identify properties of isosceles trapezoids                               quadrilaterals
                           the properties of isosceles trapezoids          *determine properties of isosceles trapezoids with respect to parallel     trapezoid
                           • Same properties as trapezoids                 sides, length of sides, diagonal measurements, and measurement of          isosceles trapezoid
                           • Non-parallel opposite sides (legs) are        angles                                                                     consecutive sides/angles
                           congruent                                       *explore isosceles trapezoids and their properties to verify the type of   opposite sides/angles
                           • Base angles are congruent                     figure formed                                                              midsegments
                           • Diagonals are congruent                                                                                                  diagonals


Resources:                 G. 8-6 pg.439; supplemental with patty paper

Assessments:
                           click here
R.4.G.1i                   Explore, verify and solve problems involving    *identify properties of kites                                              quadrilaterals
                           the properties of kites                         *determine properties of kites with respect to parallel sides, length of   kite
                           • Quadrilateral                                 sides, diagonal measurements, and measurement of angles                    consecutive sides/angles
                           • Two pairs of adjacent sides are congruent     *explore kites and their properties to verify the type of figure formed    opposite sides/angles
                           • No opposite sides are congruent                                                                                          diagonals
                           • Diagonals are perpendicular                                                                                              perpendicular



Resources:                 wkst Classifying Quadrilaterals; wkst Diagonals of Quadrilaterals; wkst Identifying Attributes of Quadrilaterals


Assessments:
                           click here
5b. Essential Question - How are the properties of polygons used to find angle measures and number of sides?
R.4.G.2a                   Solve problems involving the sum of the         *classify polygons based on the number of sides                            polygons
                           measures of the interior angles of a polygon    *identify regular and irregular polygons                                   consecutive sides
                           and the interior angle measure of regular and   *identify concave and convex polygons                                      interior angles of a polygon
                           irregular polygons                              *determine the sum of the interior angles of several polygons to derive    regular polygon, including
                                                                           the formula                                                                pentagon, hexagon, heptagon,
                                                                           *use the formula for determining the sum of the interior angles            octagon, decagon
                                                                           *calculate an interior angle of a regular polygons                         irregular polygon
                                                                           *calculate a missing interior angle of a polygon given the other angles    concave polygon
                                                                           *given the total degrees of the interior angles, determine the number of   convex polygon
                                                                           sides or angles of a polygon
                                                                           *solve problems using properties of polygons

Resources:                 G. 8-1 pg.404; Manipulatives pg.128; Ch.8 Resources pg.422; wkst. Concave and Convex Polygons; wkst Finding the Sum of the Interior Angles of a
                           Polygon; wkst The Big Quadrilateral Puzzle; patty paper wkst 56




           Page 19 of 40                                                               Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
Assessments:
                           click here
R.4.G.2b                   Solve problems involving the exterior angles   *recognize that the sum of exterior angles of any polygon is 360 degrees     polygons
                           of a regular or irregular polygon              *calculate an exterior angle of a regular polygons                           consecutive sides
                                                                          *calculate a missing exterior angle of a polygon given the other angles      interior angles of a polygon
                                                                          *given the total degrees of each exterior angle, determine the number of     exterior angle of a polygon
                                                                          sides or angles of a polygon                                                 regular polygon, including
                                                                          *solve problems using properties of polygons                                 pentagon, hexagon, heptagon,
                                                                                                                                                       octagon, decagon
                                                                                                                                                       irregular polygon
                                                                                                                                                       concave polygon
                                                                                                                                                       convex polygon

Resources:                 G. 8-1 pg.404; Ch.8 Resources pg.418; wkst Polygons and Formulas


Assessments:
                           click here
R.4.G.2c                   Solve problems involving the number of sides *calculate a missing interior or exterior angle of a polygon given the other   polygons
                           and number of angles of a polygon            angles                                                                         consecutive sides
                                                                        *given the total degrees of the interior angles, or the degrees of each        interior angles of a polygon
                                                                        exterior angle, determine the number of sides or angles of a polygon           exterior angle of a polygon
                                                                        *solve problems using properties of polygons                                   regular polygon, including
                                                                                                                                                       pentagon, hexagon, heptagon,
                                                                                                                                                       octagon, decagon
                                                                                                                                                       irregular polygon
                                                                                                                                                       concave polygon
                                                                                                                                                       convex polygon

Resources:                 G. 8-1 pg.404; problems pg.407 21-26

Assessments:
                           click here
5c. Essential Question - What determines a polygon and how are they used?




           Page 20 of 40                                                              Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
CGT.5.G.5                 Based on properties of polygons, determine      *classify polygons based on their properties                                  parallelogram
                          the type of figure formed from a given set of   *use the distance formula to determine lengths of sides and diagonals of      isosceles triangle
                          points                                          a polygon                                                                     trapezoid
                                                                          *use the slope formula to determine parallel and perpendicular sides and      rectangle
                                                                          diagonals of polygons                                                         square
                                                                          *determine the types of figures based on their properties, when given a       rhombus
                                                                          set of points plotted in the coordinate plane                                 scalene triangle
                                                                                                                                                        equilateral triangle
                                                                                                                                                        kite
                                                                                                                                                        regular polygons
                                                                                                                                                        distance formula
                                                                                                                                                        slope formula
                                                                                                                                                        slopes of parallel and or
                                                                                                                                                        perpendicular lines
National Core:            G.SRT.1                                         Verify experimentally the properties of dilations given by a center and
                                                                          a scale factor: (a.) A dilation takes a line not passing through the center
                                                                          of the dilation to a parallel line, and leaves a line passing through the
                                                                          center unchanged. (b.) The dilation of a line segment is longer or shorter
                                                                          in the ratio given by the scale factor.


Resources:                G. 8-7 pg.447; pg.429 problems 27-29; pg.437 problems 53-56; pg.442 problems 9-12; Ch.8 Resource pg.442; wkst. Coordinating Polygons


Assessments:
                          click here
20 SLEs                                                                                                                                                                     End of Module 1


ALIGNMENT NOTES
                                                                                        Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
                                                                                Project for Module 4




          Page 21 of 40                                                               Glencoe Geometry: 2005                                                   127rgeorge@pcssdmail.org
GEOMETRY                  PULASKI CO. SPEC. SCHOOL DIST.                                                                                                          2010 - 2011
Module 5     Start: 2/7/2011 Teaching Days: 22              Test: 3/17/2011      Remediation Days: 1 End: 3/11/2011
                Student Learning Expectation                                                    Task Analysis                                              Vocabulary

6. Enduring Understanding - Geometric transformations form mappings.
6a. Essential Question - How are geometric transformations mapped from the preimage to the image?
CGT.5.G.7a              Draw and interpret the results of              *define translation, reflection, and rotation                             transformation
                        transformations on figures in the coordinate   *identify transformations                                                 line of symmetry
                        plane using translations, reflections, and     *draw translations, reflections, and rotations                            translations
                        rotations (90°, 180°, clockwise and            *draw, apply and interpret transformations transformations in the         reflections
                        counterclockwise about the origin)             coordinate plane                                                          rotations
                                                                                                                                                 clockwise
                                                                                                                                                 counter-clockwise


National Core:          G.CO.2                                         Represent transformations in the plane using, e.g., transparencies
                                                                       and geometry software; describe transformations as functions that
                                                                       take points in the plane as inputs and give other points as outputs.
                                                                       Compare transformations that preserve distance and angle to those
                                                                       that do not (e.g., translation versus horizontal stretch).




                        G.CO.5                                         Given a geometric figure and a rotation, reflection, or translation,
                                                                       draw the transformed figure using, e.g., graph paper, tracing paper, or
                                                                       geometry software. Specify a sequence of transformations that will
                                                                       carry a given figure onto another.




Resources:              G. 9-1 pg.463; 9-2 pg.470; 9-3 pg.473; 9-4 pg.483; supplemental material booklets on transformations

Assessments:
                        click here


        Page 22 of 40                                                              Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
CGT.5.G.7b              Draw and interpret the results of dilations   *define dilation                                                              dilations
                        (scale factor) and successive dilations on    *draw and interpret the results of dilations and successive dilations         successive dilations
                        figures in the coordinate plane                                                                                             scale factor




National Core:          G.SRT.1                                       Verify experimentally the properties of dilations given by a center and
                                                                      a scale factor: (a.) A dilation takes a line not passing through the center
                                                                      of the dilation to a parallel line, and leaves a line passing through the
                                                                      center unchanged. (b.) The dilation of a line segment is longer or shorter
                                                                      in the ratio given by the scale factor.




                        G.CO.2                                        Represent transformations in the plane using, e.g., transparencies
                                                                      and geometry software; describe transformations as functions that
                                                                      take points in the plane as inputs and give other points as outputs.
                                                                      Compare transformations that preserve distance and angle to those
                                                                      that do not (e.g., translation versus horizontal stretch).




                        G.CO.5                                        Given a geometric figure and a rotation, reflection, or translation,
                                                                      draw the transformed figure using, e.g., graph paper, tracing paper, or
                                                                      geometry software. Specify a sequence of transformations that will
                                                                      carry a given figure onto another.




Resources:              G. 9-5 pg.490; supplemental cartoons; wkst. Working with a Scale


Assessments:
                        click here




        Page 23 of 40                                                             Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
CGT.5.G.7c              Draw and interpret the results of successive       *define translation, reflection, rotation, and dilation                       transformation
                        transformations on figures in the coordinate       *identify transformations                                                     line of symmetry
                        plane (Ex. translations, reflections, rotations,   *draw translations, reflections, rotations, and dilations                     successive transformations
                        and dilations)                                     *draw, apply and interpret transformations and successive                     translations
                                                                           transformations in the coordinate plane                                       reflections
                                                                                                                                                         rotations
                                                                                                                                                         dilations
                                                                                                                                                         clockwise
                                                                                                                                                         counter-clockwise



National Core:          G.SRT.1                                            Verify experimentally the properties of dilations given by a center and
                                                                           a scale factor: (a.) A dilation takes a line not passing through the center
                                                                           of the dilation to a parallel line, and leaves a line passing through the
                                                                           center unchanged. (b.) The dilation of a line segment is longer or shorter
                                                                           in the ratio given by the scale factor.




                        G.CO.2                                             Represent transformations in the plane using, e.g., transparencies
                                                                           and geometry software; describe transformations as functions that
                                                                           take points in the plane as inputs and give other points as outputs.
                                                                           Compare transformations that preserve distance and angle to those
                                                                           that do not (e.g., translation versus horizontal stretch).




                        G.CO.5                                             Given a geometric figure and a rotation, reflection, or translation,
                                                                           draw the transformed figure using, e.g., graph paper, tracing paper, or
                                                                           geometry software. Specify a sequence of transformations that will
                                                                           carry a given figure onto another.




        Page 24 of 40                                                                  Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
Resources:                MCO---Students will work in groups to use graph paper or white marker boards to graph transformations. Students will discuss the strategy used and the
                          change in the x and y coordinate.


Assessments:
                          click here
7. Enduring Understanding - Attributes of geometric figures affect their ability to tessellate.
7a. Essential Question - What determines if a geometric figure will tessellate?
R.4.G.3                   Identify and explain why figures tessellate       *determine the measure of an interior angle of a polygon                tessellation
                                                                            *define tessellate
                                                                            *determine through exploration that angle measures of polygons which
                                                                            will tessellate must be factors of 360 degrees
                                                                            *identify figures which will tessellate and why


Resources:                G. 9-4 pg.483; have students do their own tessellation; patty paper wkst 180-187;     MCO---Student will research the drawings of Dutch artist M.C. Escher
                          and create their own tesselation.


Assessments:
                          click here
4. Enduring Understanding - Indirect measure is based on properties of geometric figures
4c. Essential Question - How are areas of ploygons and circles related and applied?
M.3.G.1                   Calculate probabilities arising in geometric      *write ratios                                                           probability
                          contexts (Ex. find the probability of hitting a   *find perimeter and areas of polygons                                   area
                          particular ring on a dartboard)                   *find circumference and areas of circles                                ratio
                                                                            *compare area, perimeter, and circumference of basic shapes
                                                                            *use ratios to find percentages
                                                                            *solve proportions to find probability of hitting a target

Resources:                G. 11-5 pg.622 ; MCO----Student will use shaded parts of a game board (darts, checkers, etc) or scale drawing of a tennis or basketball court to calculate
                          the probabilities.


Assessments:
                          click here
8. Enduring Understanding - Three dimensional figures have properties similar to those of 2 dimensional figures.

8a. Essential Question - How are two-dimensional relationships connected to properties of three-dimensional figures?

          Page 25 of 40                                                                Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
R.4.G.4                    Identify the attributes of the five Platonic     *recognize and name the five platonic solids                              platonic solids
                           Solids                                           *identify the polygons that form the faces of the platonic solids         tetrahedron
                                                                            *define faces, vertices, and edges and determine the number of each for   dodecahedron
                                                                            the platonic solids                                                       icosahedron
                                                                            *identify the attributes of the five platonic solids                      hexahedron
                                                                                                                                                      octahedron
                                                                                                                                                      cube
                                                                                                                                                      regular polyhedron
                                                                                                                                                      faces, edges, vertices (review-had
                                                                                                                                                      since 4th grade)


Resources:                 G. 12-1 pg.636; supplemental nets and figures; wkst Types of Solids

Assessments:
                           click here
R.4.G.7a                   Use orthographic drawings (top, front, side) to *given views of a three-dimensional object, draw and/or identify the       foundation drawing
                           represent three-dimensional objects             complete object                                                            orthographic drawing
                                                                           *draw the 2-dimensional and foundation views of three-dimensional
                                                                           objects

Resources:
Assessments:
                           click here
R.4.G.7b                   Use isometric drawings (corner) to represent     *given views of a three-dimensional object, draw and/or identify the      isometric drawing
                           three-dimensional objects                        complete object
                                                                            *draw the views of three-dimensional objects
                                                                            *draw and interpret isometric drawings


Resources:                 G. 12-1 pg.640; Ch.12 Resources pg.666;        MCO----Students will work in groups to make orthographic and isometic drawing using stacked blocks and
                           isometric dot paper.


Assessments:
                           click here




           Page 26 of 40                                                               Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
R.4.G.8                   Draw, examine, and classify cross-sections of Prerequisite Skills:                                                        cross-section
                          three-dimensional objects                     •identify three-dimensional figures
                                                                        •identify polygons and circles

                                                                          *identify ellipses
                                                                          *draw cross-sections of three- dimensional objects
                                                                          *examine and classify by naming the resulting two-dimensional cross-
                                                                          section
                                                                          *draw and classify the results of cross-sections of three-dimensional
                                                                          objects


National Core:            G.GMD.4                                         Identify the shapes of two-dimensional cross-sections of three-
                                                                          dimensional objects, and identify three-dimensional objects generated
                                                                          by rotations of two-dimensional objects.



Resources:                G. 12-1 pg.640; problems pg.640 25-30; MCO---- Students will work in groups to make cross-sections using Play-DOh or Styrofoam.

Assessments:
                          click here
9. Enduring Understanding - Practical problems can be interpreted, represented, and solved using formulas.

9a. Essential Question - How are geometric formulas applied to solve basic and application problems.

M.3.G.2b                  Solve application problems involving area of    *use estimations and exact values in area of circles                      area
                          circles, polygons and composite figures using   *convert between units of measure                                         polygon
                          appropriate units and formulas and expressing   *substitute and evaluate expressions                                      circle
                          solutions in both approximate and exact forms   *recognize two-dimensional figures                                        composite figure
                          (include apothem of a regular polygon)          *use square unit representation, and understand when it is used           apothem
                                                                          *apply appropriate formulas to find area of two- dimensional shapes and   concentric circles
                                                                          composite shapes (Resource: EOC Mathematics Reference Sheet)
                                                                          *solve application problems




National Core:            G.MG.2                                          Apply concepts of density based on area and volume in modeling
                                                                          situations (e.g., persons per square mile, BTUs per cubic foot).


Resources:                Area:G. 11-1 pg.595; 11-2 pg.601; 11-3 pg.610; pg.11-4 pg.617; geoboards; wkst. Finding Area- Painting a Room; wkst. Finding Area-Tiling a Floor; wkst
                          Finding Area-Fertilizing a Lawn; wkst. Comparing Areas; patty paper wkst 205


          Page 27 of 40                                                              Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
Assessments:
                           click here
M.3.G.2c                   Solve application problems involving surface     *use estimations and exact values in finding surface area               area
                           area of prisms, cylinders, pyramids, and cones   *convert between units of measure                                       surface area
                           using appropriate units and formulas and         *substitute and evaluate expressions                                    polygon
                           expressing solutions in both approximate and     *recognize two- and three-dimensional figures                           prism
                           exact forms                                      *use square unit representation, and understand when it is used         pyramid
                                                                            *apply appropriate formulas to find surface area of three-dimensional   cone
                                                                            shapes and composite shapes (Resource: EOC Mathematics Reference        cylinder
                                                                            Sheet)                                                                  composite figure
                                                                            *solve application problems                                             apothem
                                                                                                                                                    concentric circles
National Core:             G.MG.2                                           Apply concepts of density based on area and volume in modeling
                                                                            situations (e.g., persons per square mile, BTUs per cubic foot).

Resources:                 Surface Area: G. 12-2 pg.643; 12-3 pg.649; 12-4 pg.655; 12-5 pg.660; 12-6 pg.666; 12-1 pg. 636 use nets to make 3-dimensional figures; wkst. Surface
                           Area and Wrapping Paper;; MCO---- Students will work in groups to measure and find the surface area and volume of various empty food containers.

Assessments:
                           click here
M.3.G.2d                   Solve application problems involving surface     *use estimation and exact values when finding surface area              area
                           area of composite figures using appropriate      *convert between units or measure                                       surface area
                           units and formulas and expressing solutions in   *substitute and evaluate expressions                                    polygon
                           both approximate and exact forms                 *recognize two- and three-dimensional figures                           prism
                                                                            *use square unit representation, and understand when itis used          pyramid
                                                                            *apply appropriate formulas to find surface area of three-dimensional   cone
                                                                            shapes and composite shapes (Resource: EOC Mathematics Reference        cylinder
                                                                            Sheet)                                                                  sphere
                                                                            *solve application problems                                             composite figure
                                                                                                                                                    apothem
                                                                                                                                                    concentric circles
National Core:             G.MG.2                                           Apply concepts of density based on area and volume in modeling
                                                                            situations (e.g., persons per square mile, BTUs per cubic foot).
Resources:                 Surface Area: G. 12-2 pg.643; 12-3 pg.649; 12-4 pg.655; 12-5 pg.660; 12-6 pg.666; 12-1 pg. 636 use nets to make 3-dimensional figures; wkst. Surface
                           Area and Wrapping Paper;; MCO---- Students will work in groups to measure and find the surface area and volume of various empty food containers.

Assessments:
                           click here
12 SLEs                                                                                                                                                                  End of Module 1


ALIGNMENT NOTES
                                                                                          Notation


           Page 28 of 40                                                               Glencoe Geometry: 2005                                              127rgeorge@pcssdmail.org
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
                                             Project for Module 5




        Page 29 of 40                           Glencoe Geometry: 2005   127rgeorge@pcssdmail.org
GEOMETRY                     PULASKI CO. SPEC. SCHOOL DIST.                                                                                                              2010 - 2011
Module 6       Start: 2/14/2011 Teaching Days: 28               Test: 5/5/2011       Remediation Days: 1 End: 5/5/2011
                  Student Learning Expectation                                                      Task Analysis                                              Vocabulary
9. Enduring Understanding - Practical problems can be interpreted, represented, and solved using formulas.

9a cont.. Essential Question - How are geometric formulas applied to solve basic and application problems.

M.3.G.2e                   Solve application problems involving volume     *use estimations and exact values when finding volume                    volume
                           of prisms, cylinders, pyramids, and cones       *convert between units of measure                                        polygon
                           using appropriate units and formulas and        *substitute and evaluate expressions                                     prism
                           expressing solutions in both approximate and    *recognize three-dimensional figures                                     pyramid
                           exact forms                                     *use cubic unit representation, and understand when it is used           cone
                                                                           *apply appropriate formulas to find volume of three-dimensional shapes   cylinder
                                                                           and composite shapes (Resource: EOC Mathematics Reference Sheet)         composite figure
                                                                           *solve application problems                                              apothem
                                                                                                                                                    concentric circles
National Core:             G.GMD.3                                      Use volume formulas for cylinders, pyramids, cones, and spheres to
                                                                        solve problems.
Resources:                 Volume: G. 13-1 pg.688; 13-2 pg.696; differentiated instruction pg.698; teacher to teacher pg.699; wkst. Volumes of Containers;

Assessments:
                           click here
M.3.G.2f                   Solve application problems involving volume     *use estimations and exact values when finding volume                    volume
                           of composite figures using appropriate units    *convert between units of measure                                        polygon
                           and formulas and expressing solutions in both   *substitute and evaluate expressions                                     prism
                           approximate and exact forms                     *recognize three-dimensional figures                                     pyramid
                                                                           *use cubic unit representation, and understand when it is used           cone
                                                                           *apply appropriate formulas to find volume of three-dimensional shapes   cylinder
                                                                           and composite shapes (Resource: EOC Mathematics Reference Sheet)         sphere
                                                                           *solve application problems                                              composite figure
                                                                                                                                                    apothem
                                                                                                                                                    concentric circles
National Core:             G.GMD.3                                         Use volume formulas for cylinders, pyramids, cones, and spheres to
                                                                           solve problems.
Resources:                 G.pg.699 problems 17-19

Assessments:
                           click here




           Page 30 of 40                                                              Glencoe Geometry: 2005                                               127rgeorge@pcssdmail.org
M.3.G.2g                   Solve application problems involving surface     *use estimations and exact values in surface area and volume of spheres         area
                           area and volume of spheres using appropriate     *convert between units of measure                                               volume
                           units and formulas and expressing solutions in   *substitute and evaluate expressions                                            surface area
                           both approximate and exact forms                 *recognize three-dimensional figures                                            polygon
                                                                            *use square and cubic unit representation, and understand when each is          sphere
                                                                            used                                                                            composite figure
                                                                            *apply appropriate formulas to find volume and surface area of three-           apothem
                                                                            dimensional shapes and composite shapes (Resource: EOC Mathematics              concentric circles
                                                                            Reference Sheet)
                                                                            *solve application problems

National Core:             G.GMD.3                                          Use volume formulas for cylinders, pyramids, cones, and spheres to
                                                                            solve problems.
                           G.GMD.2                                          (+) Give an informal argument using Cavalieri’s principle for the
                                                                            formulas for the volume of a sphere and other solid figures.

Resources:                 G. 12-7 pg.671; 13-3 pg.703; wkst. Creating Problems and Applying Formulas (Advanced); MCO---Investigate careers in the U.S. and other cultures that
                           solve problems of area, perimeter and volume.

Assessments:
                           click here
10. Enduring Understanding - Relationships exist among angles, arcs, and segments of circles.

10a. Essential Question - How are circle formulas applied to solve basic and application problems.

R.4.G.5a                   Solve problems involving the measure of          *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
                           central angles, the relationship between         *apply relationships of congruent chords and their arcs, and use those          inscribed angle
                           congruent central angles , the relationship      relationships to solve problems                                                 arc
                           between congruent chords and the measure         *apply relationship of central angles and their arcs to solve problems          chord
                           of the arcs they intercept and vice versa        *calculate angles and arc measures of interior angles of a circle               circle
                                                                                                                                                            point of tangency
                                                                                                                                                            radius
                                                                                                                                                            diameter

National Core:             G.C.1                                            Prove that all circles are similar.
                           G.C.2                                            Identify and describe relationships among inscribed angles, radii,
                                                                            and chords. Include the relationship between central, inscribed, and
                                                                            circumscribed angles; inscribed angles on a diameter are right angles;
                                                                            the radius of a circle is perpendicular to the tangent where the radius
                                                                            intersects the circle.

                           G.C.3                                            Construct the inscribed and circumscribed circles of a triangle, and
                                                                            prove properties of angles for a quadrilateral inscribed in a circle.


           Page 31 of 40                                                                 Glencoe Geometry: 2005                                                    127rgeorge@pcssdmail.org
Resources:                 G. 10-2 pg.529; wkst Drawing Circles; wkst Circles:Symbols of Segments and Angles; wkst The Big Circle Puzzle

Assessments:
                           click here
R.4.G.5b                   Solve problems involving the relationship         *identify chords, central angles, radii, interior angles, and arcs            central angle
                           between a radius that is perpendicular to a       *apply relationship of central angles and their arcs to solve problems        inscribed angle
                           chord in a circle and the size of the resulting   *calculate angles and arc measures of interior angles of a circle involving   arc
                           segments of the chord                             the relationship between a radius that is perpendicular to a chord            chord
                                                                                                                                                           circle
                                                                                                                                                           radius
                                                                                                                                                           diameter
                                                                                                                                                           perpendicular
National Core:             G.C.1                                             Prove that all circles are similar.
                           G.C.2                                             Identify and describe relationships among inscribed angles, radii,
                                                                             and chords. Include the relationship between central, inscribed, and
                                                                             circumscribed angles; inscribed angles on a diameter are right angles;
                                                                             the radius of a circle is perpendicular to the tangent where the radius
                                                                             intersects the circle.

                           G.C.3                                             Construct the inscribed and circumscribed circles of a triangle, and
                                                                             prove properties of angles for a quadrilateral inscribed in a circle.

Resources:                 G. 10-3 pg.536; Manipulatives pg.164; MCO---Students will be given regular triangles, squares, pentagons, etc. to cut out. At a vertex point on another
                           sheet of paper, students will gllue a shape around the point to see if there is a gap or overlap. Students will find the measure of an interior angle and divide
                           into 360. Repeat the process for all polygons.
Assessments:
                           click here
R.4.G.5c                   Solve problems involving the congruence          *identify chords and arcs                                                      central angle
                           relationship of two chords in a circle which are *understand relationships of congruent chords and their arcs, and use          inscribed angle
                           equidistant from the center and vice versa       those relationships to solve problems                                          arc
                                                                            *calculate chords and arc measures of a circle                                 chord
                                                                                                                                                           circle
                                                                                                                                                           radius
                                                                                                                                                           diameter

National Core:             G.C.1                                             Prove that all circles are similar.
                           G.C.2                                             Identify and describe relationships among inscribed angles, radii,
                                                                             and chords. Include the relationship between central, inscribed, and
                                                                             circumscribed angles; inscribed angles on a diameter are right angles;
                                                                             the radius of a circle is perpendicular to the tangent where the radius
                                                                             intersects the circle.

                           G.C.3                                             Construct the inscribed and circumscribed circles of a triangle, and
                                                                             prove properties of angles for a quadrilateral inscribed in a circle.


           Page 32 of 40                                                                  Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
Resources:                 G. 10-3 pg.536

Assessments:
                           click here
R.4.G.5d                   Solve problems involving the relationship       *identify chords, central angles, interior angles, inscribed angles, and arcs central angle
                           between measure of an angle inscribed in a      *apply relationship of central angles and their arcs to solve problems        inscribed angle
                           circle and the measure of the intercepted arc   involving inscribed angles                                                    arc
                                                                           *calculate angles and arc measures of inscribed angles of a circle            chord
                                                                                                                                                         circle
                                                                                                                                                         radius
                                                                                                                                                         diameter

National Core:             G.C.1                                           Prove that all circles are similar.
                           G.C.2                                           Identify and describe relationships among inscribed angles, radii,
                                                                           and chords. Include the relationship between central, inscribed, and
                                                                           circumscribed angles; inscribed angles on a diameter are right angles;
                                                                           the radius of a circle is perpendicular to the tangent where the radius
                                                                           intersects the circle.

                           G.C.3                                           Construct the inscribed and circumscribed circles of a triangle, and
                                                                           prove properties of angles for a quadrilateral inscribed in a circle.
Resources:                 G. 10-4 pg.544; Manipulatives pg.167-169

Assessments:
                           click here
R.4.G.5e                   Solve problems involving the perpendicular     *identify central angles, interior angles, and arcs                           central angle
                           relationship between a tangent to a circle and *understand relationship of central angles and their arcs                     arc
                           a radius drawn to the point of tangency        *identify tangents of a circle                                                tangent
                                                                          *define point of tangency                                                     tangent to a circle
                                                                          *apply the relationship between a tangent and a radius or diameter at         circle
                                                                          point of tangency, and use that relationship to solve problems                point of tangency
                                                                                                                                                        radius
                                                                                                                                                        diameter
                                                                                                                                                        perpendicular
National Core:             G.C.4                                           (+) Construct a tangent line from a point outside a given circle to the
                                                                           circle.
Resources:                 G. 10-5 pg.552; Manipulatives pg.174-175; Ch.10 Resources pg.569; wkst Tangents: Circles and Lines; wkst. The Bigger Circle Puzzle

Assessments:
                           click here




           Page 33 of 40                                                               Glencoe Geometry: 2005                                                  127rgeorge@pcssdmail.org
R.4.G.5f                   Solve problems involving the congruence of   *identify interior angles, inscribed angles, and arcs                            central angle
                           two segments from the same exterior point of *apply relationship of central angles and their arcs to solve problems           inscribed angle
                           a circle that are tangent to a circle        involving tangents to a circle from a common point                               arc
                                                                        *recognize tangents of a circle                                                  tangent
                                                                        *define point of tangency                                                        tangent to a circle
                                                                        *apply relationships of tangents and use those relationships to solve            circle
                                                                        problems                                                                         point of tangency
                                                                                                                                                         radius
                                                                                                                                                         diameter

National Core:             G.C.4                                         (+) Construct a tangent line from a point outside a given circle to the
                                                                         circle.
Resources:                 G. 10-5 pg.552; Ch.10 Resources pg.568

Assessments:
                           click here
R.4.G.5g                   Solve problems involving the measure of an    *identify chords, central angles, interior angles, and arcs                     central angle
                           angle formed by the intersection of two       *apply relationships of congruent chords and their arcs, and use those          inscribed angle
                           chords within a circle                        relationships to solve problems                                                 arc
                                                                         *apply relationship of central angles and their arcs                            chord
                                                                         *calculate angles and arc measures of interior angles of a circle               circle
                                                                                                                                                         radius
                                                                                                                                                         diameter

Resources:                 G. 10-6 pg.561; problems pg,564 12-15,20
Assessments:
                           click here
R.4.G.5h                   Solve problems involving the measure of an    *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
                           angle formed by a secant and a tangent        *apply relationships of congruent chords and their arcs, and use those          inscribed angle
                           intersecting at the point of tangency         relationships to solve problems                                                 arc
                                                                         *apply relationship of central angles and their arcs to calculate angles and    chord
                                                                         arc measures of interior angles of a circle                                     tangent
                                                                         *identify tangents and secants of a circle                                      tangent to a circle
                                                                         *define point of tangency                                                       secant
                                                                         *understand relationships of tangent and secant segments, and use those         circle
                                                                         relationships to solve problems                                                 point of tangency
                                                                                                                                                         radius
                                                                                                                                                         diameter
Resources:                 G. 10-6 pg.561; Ch.10 Resources pg.576
Assessments:
                           click here


           Page 34 of 40                                                             Glencoe Geometry: 2005                                                     127rgeorge@pcssdmail.org
R.4.G.5i                   Solve problems involving the measure of an      *identify chords, secents, tangents, and arcs                                   arc
                           angle formed by two intersecting secants, a     *identify tangents and secants of a circle                                      tangent
                           secant and a tangent, or two tangents           *define point of tangency                                                       tangent to a circle
                           intersecting in the exterior of a circle        *apply relationships of tangent and secant segments, and use those              secant
                                                                           relationships to solve problems                                                 point of tangency
                                                                                                                                                           radius
                                                                                                                                                           diameter

National Core:             G.C.4                                          (+) Construct a tangent line from a point outside a given circle to the
                                                                          circle.
Resources:                 G. 10-6 pg.561; wkst. The Biggest Circle Puzzle
Assessments:
                           click here
R.4.G.5j                   Solve problems involving the measure of the     *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
                           segments formed by two intersecting chords      *understand relationships of congruent chords and their arcs, and use           inscribed angle
                           in a circle                                     those relationships to solve problems                                           arc
                                                                           *understand relationship of central angles and their arcs                       chord
                                                                           *calculate segment lengths of intersecting chords of a circle                   circle
                                                                                                                                                           radius
                                                                                                                                                           diameter

Resources:                 G. 10-7 pg.569; Ch.10 Resources pg. 582
Assessments:
                           click here
R.4.G.5k                   Solve problems involving the measure of the     *identify chords, central angles, interior angles, inscribed angles, and arcs   central angle
                           tangent segment, the secant segment, and        *understand relationships of congruent chords and their arcs, and use           inscribed angle
                           the external segment of the secant when a       those relationships to solve problems                                           arc
                           tangent and secant are drawn to a circle from   *apply relationship of central angles and their arcs to solve problems          chord
                           the same exterior point and the measure of      *identify tangents and secants of a circle                                      tangent
                           the secant segments and the external            *define point of tangency                                                       tangent to a circle
                           segments formed by two secants to a circle      *understand the relationship between a tangent and a radius or diameter         secant
                           intersecting at an external point from the      at point of tangency, and use that relationship to solve problems               circle
                           circle                                          *understand relationships of tangent and secant segments, and use those         point of tangency
                                                                           relationships to solve problems                                                 radius
                                                                                                                                                           diameter


Resources:                 G. 10-6 pg.561; G. 10-7 pg.569

Assessments:
                           click here



           Page 35 of 40                                                               Glencoe Geometry: 2005                                                     127rgeorge@pcssdmail.org
R.4.G.5l                   Solve problems involving the area of sectors    *find the area and circumference of a circle                                  circumference
                           and the lengths of arcs                         *identify sector area and arc lengh                                           central angle
                                                                           *use relationships of parts of circles to determine areas of sectors          arc
                                                                           *use the relationships of parts of circles to determine the length of a given chord
                                                                           arc                                                                           circle
                                                                                                                                                         radius
                                                                                                                                                         diameter
                                                                                                                                                         sector
Resources:                 G. pg.532; G. pg.623-624

Assessments:
                           click here
R.4.G.6                    Solve problems using inscribed and              *identify inscribed and circumscribed figures                               inscribed figure (circle or polygon)
                           circumscribed figures                           *find areas of polygons and circles to solve problems                       circumscribed figure (circle or
                                                                           *find incenter and circumcenter of triangles                                polygon)
                                                                           *solve problems using inscribed and circumscribed figures                   incenter
                                                                                                                                                       circumcenter

National Core:             G.CO.13                                         Construct an equilateral triangle, a square, and a regular hexagon
                                                                           inscribed in a circle.
Resources:                 G. 11-3 pg. 610; Manipulatives pg.185; wkst Inscribed Polygons
Assessments:
                           click here
M.3.G.2a                   Solve application problems involving            Prerequisite Skills:                                                        circumference
                           circumference, and perimeter of polygons and    •use estimations and exact values in circumference of circles               perimeter
                           composite figures using appropriate units and   •convert between units of measure                                           polygon
                           formulas and expressing solutions in both       •substitute and evaluate expressions                                        circle
                           approximate and exact forms                     •recognize two-dimensional figures                                          composite figure
                                                                           •use linear unit representation, and understand when it is used             apothem
                                                                                                                                                       concentric circles
                                                                           *apply appropriate formulas to find perimeter/circumference of two-
                                                                           dimensional shapes and composite shapes (Resource: EOC Mathematics
                                                                           Reference Sheet)
                                                                           *solve application problems
Resources:                 G. Ch.1 Resource pg 36; 10-1 pg.522; Manipulatives pg.161 find pi using circles(donuts,cookies,soda cans, use dental floss for measurement tool with
                           rulers); wkst. Finding perimeter -Fencing a Yard;

Assessments:
                           click here
11a. Essential Question - How can the relationship between points on a circle be described in the coordinate plane?




           Page 36 of 40                                                               Glencoe Geometry: 2005                                                 127rgeorge@pcssdmail.org
CGT.5.G.6a                Write the equation of a circle in standard form *recognize the standard form of the equation of a circle                   standard form of an equation for
                          given a graph on a coordinate plane and vice *identify the center of a circle and determine the length of its radius given a circle
                          versa                                           a graph                                                                    circle
                                                                          *write the standard form of the equation of the circle                     center of a circle
                                                                          *use the Pythagorean Theorem to derive the standard form of the            radius
                                                                          equation of a circle                                                       diameter
National Core:            G.GPE.1                                         Derive the equation of a circle of given center and radius using the
                                                                          Pythagorean Theorem; complete the square to find the center and
                                                                          radius of a circle given by an equation.
Resources:                G. 10-8 pg.575
Assessments:
                          click here
CGT.5.G.6b                Write the equation of a circle in standard form *recognize the standard form of the equation of a circle                   standard form of an equation for
                          given the center and radius and vice versa      *write the standard form of the equation of a circle given the center and a circle
                                                                          radius                                                                     circle
                                                                          *write the standard form of the equation of the circle                     center of a circle
                                                                          *use the distance formula to derive the standard form of the equation of a radius
                                                                          circle                                                                     diameter
National Core:            G.GPE.1                                        Derive the equation of a circle of given center and radius using the
                                                                         Pythagorean Theorem; complete the square to find the center and
                                                                         radius of a circle given by an equation.
Assessments:
                          click here
18 SLEs                                                                                                                                                                  End of Module 1




ALIGNMENT NOTES
                                                                                       Notation
G.- Glencoe Textbook;
wkst - worksheet included;
All caps - group work from Get It Together
                                                                               Project for Module 6




          Page 37 of 40                                                              Glencoe Geometry: 2005                                                127rgeorge@pcssdmail.org
Click on the links to open the following
                PDF files

      8_by_8_numbered_grids

    10_by_10_numbered_grids

        grids_not_numbered

     graphing_calculator_grids

           isometric_grids

        6_square_dot_grids

             logic_grids

         plain_graph_paper

          notebook_paper
EOC Mathematics Reference Sheet
GEOMETRY   PULASKI CO. SPEC. SCHOOL DIST.   2010-2011

          National Core Standards
 NOT CURRENTLY PLACED IN THE CURRICULUM

								
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